P455 Introduction to Phase Transitions and Critical phenomena

Course No: 
P301 (Statistical Mechanics)

(42 Lectures + 14 Tutorial)

  1. Introduction to critical phenomena and first order phase transition. Survey of experimental results and scaling hypothesis, introduction to critical exponents and universality.
  2. Review of thermodynamic potentials, introduction to order parameter and response functions.
  3. Introduction to interacting systems: study of one dimensional Ising model via transfer matrix, lack of phase transition in one dimension, study of Ising model in two dimensions, XY and Heisenberg model.
  4. Mean field theory: calculation of order parameter, response functions and correlation functions using Curie-Weiss mean field theory and Landau-Ginzberg theory, calculation of critical exponents for mean field systems, range of validity of mean field theory.
  5. Introduction to re-normalization group (RG): Kadanoff block spins and real space RG methods, Perturbative RG in momentum space: Wilson-Fisher RG and epsilon expansion, broken continuous symmetry: Mermin Wagner theorem, Goldstone modes and Kosterlitz Thouless phase transition, introduction to non-linear sigma models, quantum critical phenomena and quantum phase transitions, introduction to 1D Transverse Field Ising Model and introduction to Bose- Hubbard model.
Reference Books: 
  1. Introduction to phase Transitions and Critical phenomena by H. Eugene Stanley
  2. Modern approach to Critical phenomena by Igor Herbut
  3. Statistical physics: Statics, Dynamics and Renormalization by Leo p. Kadanoff
  4. The Theory of Critical phenomena by J. J. Binney, a. J. Fisher, M. E. J. newman
  5. Modern Theory of Critical phenomena by Shang-keng Ma
  6. Statistical Mechanics of phase Transitions by J. Yeomans
  7. Field Theory, the Renormalisation group and Critical phenomena by Daniel J.  Amit
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